Rashford was again the hero for United with an extra-time winner in their Europa League quarter-final against Anderlecht on Thursday night after the 19-year-old found the mark in the Premier League victory over Chelsea last weekend.
The striker continues to improve after bursting onto the scene last season, and Scholes says the sky's the limit for the teenager.
"Rashford will be a brilliant centre-forward, there is no doubt about that," Scholes told the BBC.
"His pace is incredible. He's almost the club's most important player now at the age of 19.
"What we saw against Anderlecht was that raw pace, the excitement, skill and ability to fly past people as if they are not there.
"He probably needs to work on his composure with the chances he is getting, start putting his chances away - I am sure he will.
"He has always been a centre-forward. When I saw him playing for the young United teams, he was scoring 30-40 goals a season. I know this lad can finish and score goals.
"You look at Cristiano Ronaldo's record and players like Neymar, he has that kind of ability. It is a lot to live up to, but he has that in him - he can be a world star."